Group #25015447 — subgroups

Subgroups — #25015447

Order 11008.

662 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063270	C₂	1	2	yes	maximal, complemented
2	C₂×#14583276	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582701	C₂	1	2	yes	maximal, complemented
4	#19135456	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
7	C₂²×D₃₄₄	—	2	1	no	—
8	C₂²×D₃₄₄	C₂²	1	2	yes	—
9	C₂×#13063322	—	2	1	no	—
10	C₂×#13063270	—	2	4	no	—
11	C₂×#13063270	—	2	4	no	—
12	C₂×#13063270	—	2	4	no	—
13	#14583276	—	2	4	no	—
14	C₂×#13063259	C₂²	1	1	yes	characteristic
15	C₂×#13063250	—	2	1	no	—
16	#14582805	—	2	1	no	—
17	#14582701	—	2	4	no	—
18	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₈₆	—	2	1	no	—
21	C₂²×D₁₇₂	—	2	2	no	—
22	C₂²×D₁₇₂	—	4	2	no	—
23	C₂×Dic₁₇₂	—	2	2	no	—
24	C₂×Dic₁₇₂	—	2	2	no	—
25	C₂×Dic₁₇₂	—	2	1	no	—
26	C₂×Dic₁₇₂	D₄	1	2	yes	complemented
27	C₂×D₃₄₄	—	2	2	no	—
28	C₂×D₃₄₄	—	2	2	no	—
29	C₂×D₃₄₄	—	2	2	no	—
30	C₂×D₃₄₄	—	2	2	no	—
31	C₂×D₃₄₄	—	2	4	no	—
32	C₂×D₃₄₄	—	2	2	no	—
33	C₂×D₃₄₄	—	4	2	no	—
34	C₂×D₃₄₄	—	4	2	no	—
35	C₂×D₃₄₄	D₄	1	4	yes	—
36	#13063322	—	2	4	no	—
37	#13063322	—	4	2	no	—
38	C₂×C₄⋊Dic₄₃	—	2	1	no	—
39	#13063270	—	2	16	no	—
40	#13063259	—	2	2	no	—
41	#13063250	—	4	2	no	—
42	C₄₃⋊#95	—	4	2	no	—
43	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₄₃	—	2	2	no	—
47	C₂×C₁₆×C₄₃	—	2	2	no	—
48	C₂×C₁₆×C₄₃	D₄	1	4	yes	complemented
49	C₄×C₈×C₄₃	—	2	2	no	—
50	C₂³×D₄₃	—	4	2	no	—
51	C₂²×C₄×C₄₃	D₈	1	2	yes	—
52	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×Dic₄₃	—	4	1	no	—
54	C₂²×Dic₄₃	—	4	1	no	—
55	C₂×D₁₇₂	—	2	4	no	—
56	C₂×D₁₇₂	—	4	8	no	—
57	C₂×D₁₇₂	—	4	2	no	—
58	C₂×D₁₇₂	—	4	2	no	—
59	C₂×D₁₇₂	—	4	2	no	—
60	C₂×D₁₇₂	—	4	2	no	—
61	C₂×D₁₇₂	—	4	2	no	—
62	C₂×D₁₇₂	—	8	4	no	—
63	C₂×D₁₇₂	—	8	4	no	—
64	C₂×Dic₈₆	—	2	2	no	—
65	C₂×Dic₈₆	—	4	1	no	—
66	C₂×Dic₈₆	—	4	1	no	—
67	C₂×Dic₈₆	—	4	1	no	—
68	C₂×Dic₈₆	—	4	1	no	—
69	C₂×Dic₈₆	—	4	1	no	—
70	C₂×C₈×C₄₃	—	2	1	no	—
71	C₂×C₈×C₄₃	—	2	1	no	—
72	C₂×C₈×C₄₃	D₈	1	2	yes	—
73	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
77	C₄²×C₄₃	—	2	1	no	—
78	C₄²×C₄₃	—	2	1	no	—
79	C₄⋊Dic₄₃	—	4	1	no	—
80	C₄⋊Dic₄₃	—	4	1	no	—
81	Dic₁₇₂	—	2	4	no	—
82	Dic₁₇₂	—	4	2	no	—
83	D₃₄₄	—	2	4	no	—
84	D₃₄₄	—	2	4	no	—
85	D₃₄₄	—	4	8	no	—
86	D₃₄₄	—	4	2	no	—
87	D₃₄₄	—	4	2	no	—
88	C₁₆×C₄₃	—	2	4	no	—
89	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
90	C₂²×D₄₃	—	4	4	no	—
91	C₂²×D₄₃	—	8	2	no	—
92	C₂²×D₄₃	—	8	2	no	—
93	C₂²×D₄₃	—	8	4	no	—
94	C₂²×D₄₃	—	8	4	no	—
95	C₂×C₄×C₄₃	—	2	2	no	—
96	C₂×C₄×C₄₃	—	2	2	no	—
97	C₂×C₄×C₄₃	SD₃₂	1	4	yes	complemented
98	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
99	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
100	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
101	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×Dic₄₃	—	4	2	no	—
105	C₂×Dic₄₃	—	8	1	no	—
106	C₂×Dic₄₃	—	8	1	no	—
107	C₂×Dic₄₃	—	8	1	no	—
108	C₂×Dic₄₃	—	8	2	no	—
109	D₁₇₂	—	4	4	no	—
110	D₁₇₂	—	4	4	no	—
111	D₁₇₂	—	8	16	no	—
112	D₁₇₂	—	8	2	no	—
113	D₁₇₂	—	8	2	no	—
114	Dic₈₆	—	4	2	no	—
115	Dic₈₆	—	4	2	no	—
116	Dic₈₆	—	8	1	no	—
117	Dic₈₆	—	8	1	no	—
118	C₈×C₄₃	—	2	2	no	—
119	C₈×C₄₃	#120	1	2	yes	—
120	C₈×C₄₃	#121	1	2	yes	—
121	#13328	—	43	1	no	maximal, Sylow
122	C₂²×C₄₃	#447	1	1	yes	characteristic
123	C₂²×C₄₃	#459	1	1	yes	characteristic
124	C₂²×C₄₃	#493	1	1	yes	characteristic
125	C₂²×C₄₃	C₂×SD₃₂	1	2	yes	—
126	C₂²×C₄₃	#509	1	2	yes	—
127	C₂×D₄₃	—	8	8	no	—
128	C₂×D₄₃	—	8	4	no	—
129	C₂×D₄₃	—	16	4	no	—
130	C₂×D₄₃	—	16	2	no	—
131	C₂×D₄₃	—	16	2	no	—
132	C₄×C₄₃	—	2	4	no	—
133	C₄×C₄₃	#392	1	1	yes	characteristic
134	C₄×C₄₃	#447	1	1	yes	characteristic
135	C₄×C₄₃	#459	1	1	yes	characteristic
136	C₄×C₄₃	#496	1	1	yes	characteristic
137	Dic₄₃	—	8	2	no	—
138	Dic₄₃	—	16	1	no	—
139	C₂²×SD₃₂	—	43	2	no	—
140	C₂×#493	—	43	1	no	—
141	C₂×#357	—	43	2	no	—
142	#1969	—	43	1	no	—
143	#1374	D₄₃	1	1	yes	characteristic, complemented
144	C₂×C₄₃	#2011	1	1	yes	characteristic
145	C₂×C₄₃	#2187	1	2	yes	—
146	C₂×C₄₃	#2207	1	2	yes	—
147	C₂×C₄₃	#2248	1	1	yes	characteristic
148	C₂×C₄₃	#2250	1	1	yes	characteristic
149	D₄₃	—	16	4	no	—
150	C₂²×Q₁₆	—	43	1	no	—
151	C₂²×D₈	—	43	2	no	—
152	C₂²×D₈	—	86	1	no	—
153	C₂×#127	—	86	1	no	—
154	C₂×SD₃₂	—	86	4	no	—
155	C₂×SD₃₂	—	86	4	no	—
156	C₂×SD₃₂	—	86	4	no	—
157	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
158	#493	—	86	4	no	—
159	C₂×#107	—	43	1	no	—
160	C₂×#103	—	86	1	no	—
161	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
162	#391	—	86	1	no	—
163	#357	—	86	4	no	—
164	C₄₃	#13328	1	1	yes	characteristic, complemented, Sylow
165	C₂²×Q₈	—	86	1	no	—
166	C₂²×D₄	—	86	2	no	—
167	C₂²×D₄	—	172	2	no	—
168	C₂×Q₁₆	—	43	2	no	—
169	C₂×Q₁₆	—	86	2	no	—
170	C₂×Q₁₆	—	86	2	no	—
171	C₂×Q₁₆	—	86	1	no	—
172	C₂×D₈	—	43	4	no	—
173	C₂×D₈	—	86	4	no	—
174	C₂×D₈	—	86	2	no	—
175	C₂×D₈	—	86	2	no	—
176	C₂×D₈	—	86	2	no	—
177	C₂×D₈	—	86	2	no	—
178	C₂×D₈	—	86	2	no	—
179	C₂×D₈	—	172	2	no	—
180	C₂×D₈	—	172	2	no	—
181	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
182	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
183	#127	—	86	4	no	—
184	#127	—	172	2	no	—
185	C₂×C₄⋊C₄	—	86	1	no	—
186	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
187	SD₃₂	—	86	16	no	—
188	C₂×C₁₆	—	2	2	no	—
189	C₂×C₁₆	—	2	2	no	—
190	C₂×C₁₆	D₁₇₂	1	4	yes	complemented
191	#107	—	86	2	no	—
192	#103	—	172	2	no	—
193	C₄×C₈	—	2	2	no	—
194	#95	—	172	2	no	—
195	C₂⁴	—	172	2	no	—
196	C₂×Q₈	—	86	2	no	—
197	C₂×Q₈	—	172	1	no	—
198	C₂×Q₈	—	172	1	no	—
199	C₂×Q₈	—	172	1	no	—
200	C₂×Q₈	—	172	1	no	—
201	C₂×Q₈	—	172	1	no	—
202	C₂×D₄	—	86	4	no	—
203	C₂×D₄	—	344	4	no	—
204	C₂×D₄	—	344	4	no	—
205	C₂×D₄	—	172	8	no	—
206	C₂×D₄	—	172	2	no	—
207	C₂×D₄	—	172	2	no	—
208	C₂×D₄	—	172	2	no	—
209	C₂×D₄	—	172	2	no	—
210	C₂×D₄	—	172	2	no	—
211	C₂²×C₄	—	172	1	no	—
212	C₂²×C₄	—	172	1	no	—
213	C₂²×C₄	D₃₄₄	1	2	yes	—
214	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
215	Q₁₆	—	86	4	no	—
216	Q₁₆	—	172	2	no	—
217	D₈	—	86	4	no	—
218	D₈	—	86	4	no	—
219	D₈	—	172	8	no	—
220	D₈	—	172	2	no	—
221	D₈	—	172	2	no	—
222	C₂×C₈	—	2	1	no	—
223	C₂×C₈	—	2	1	no	—
224	C₂×C₈	D₃₄₄	1	2	yes	—
225	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
226	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
227	C₂×C₈	D₄×D₄₃	1	2	yes	—
228	C₂×C₈	#10621902	1	1	yes	characteristic
229	C₄⋊C₄	—	172	1	no	—
230	C₄⋊C₄	—	172	1	no	—
231	C₄²	—	2	1	no	—
232	C₄²	—	2	1	no	—
233	C₁₆	—	2	4	no	—
234	C₂³	—	344	4	no	—
235	C₂³	—	344	4	no	—
236	C₂³	—	344	2	no	—
237	C₂³	—	344	2	no	—
238	C₂³	—	172	4	no	—
239	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
240	Q₈	—	344	1	no	—
241	Q₈	—	344	1	no	—
242	Q₈	—	172	2	no	—
243	Q₈	—	172	2	no	—
244	D₄	—	344	16	no	—
245	D₄	—	344	2	no	—
246	D₄	—	344	2	no	—
247	D₄	—	172	4	no	—
248	D₄	—	172	4	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	344	1	no	—
252	C₂×C₄	—	344	1	no	—
253	C₂×C₄	—	344	2	no	—
254	C₂×C₄	—	344	1	no	—
255	C₂×C₄	—	172	2	no	—
256	C₂×C₄	#13063270	1	4	yes	complemented
257	C₂×C₄	#13063295	1	1	yes	characteristic
258	C₂×C₄	#13063300	1	1	yes	characteristic
259	C₂×C₄	#13063322	1	1	yes	characteristic
260	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
261	C₂×C₄	#13063353	1	1	yes	characteristic
262	C₂×C₄	#13063353	1	1	yes	characteristic
263	C₈	—	2	2	no	—
264	C₈	#13063295	1	2	yes	—
265	C₈	#13063300	1	2	yes	—
266	C₂²	—	344	8	no	—
267	C₂²	—	344	4	no	—
268	C₂²	—	688	2	no	—
269	C₂²	—	688	2	no	—
270	C₂²	—	688	4	no	—
271	C₂²	#14583035	1	1	yes	characteristic
272	C₂²	#14583095	1	1	yes	characteristic
273	C₂²	#14583276	1	1	yes	characteristic
274	C₂²	C₂×#13063270	1	2	yes	—
275	C₂²	#14583337	1	2	yes	—
276	C₄	—	2	4	no	—
277	C₄	—	344	2	no	—
278	C₄	—	688	1	no	—
279	C₄	#14582809	1	1	yes	characteristic
280	C₄	#14583035	1	1	yes	characteristic
281	C₄	#14583095	1	1	yes	characteristic
282	C₄	#14583288	1	1	yes	characteristic
283	C₂	—	688	4	no	—
284	C₂	#19135668	1	1	yes	characteristic
285	C₂	#19136526	1	2	yes	—
286	C₂	#19136636	1	2	yes	—
287	C₂	#19136851	1	1	yes	characteristic
288	C₂	#19136861	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#13063270

C₂

yes

maximal, complemented

C₂×#14583276

C₂

yes

maximal, characteristic

C₂×#14582701

C₂

yes

maximal, complemented

#19135456

C₂

yes

maximal, characteristic, complemented

C₄₃×#1374

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₁₇₂

C₂²

yes

characteristic

C₂²×D₃₄₄

—

C₂²×D₃₄₄

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

—

—

C₂²×C₁₆×C₄₃

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂²×D₁₇₂

—

C₂²×D₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

D₄

yes

complemented

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

D₄

yes

—

#13063322

—

#13063322

—

C₂×C₄⋊Dic₄₃

—

#13063270

—

#13063259

—

#13063250

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

complemented

C₄×C₈×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

D₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₈

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

—

C₂×C₈×C₄₃

#41

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

SD₃₂

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

100

C₂×C₄×C₄₃

#127

yes

characteristic

101

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

102

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

103

C₂×C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

104

C₂×Dic₄₃

—

105

C₂×Dic₄₃

—

106

C₂×Dic₄₃

—

107

C₂×Dic₄₃

—

108

C₂×Dic₄₃

—

109

D₁₇₂

—

110

D₁₇₂

—

111

D₁₇₂

—

112

D₁₇₂

—

113

D₁₇₂

—

114

Dic₈₆

—

115

Dic₈₆

—

116

Dic₈₆

—

117

Dic₈₆

—

118

C₈×C₄₃

—

119

C₈×C₄₃

#120

yes

—

120

C₈×C₄₃

#121

yes

—

121

#13328

—

maximal, Sylow

122

C₂²×C₄₃

#447

yes

characteristic

123

C₂²×C₄₃

#459

yes

characteristic

124

C₂²×C₄₃

#493

yes

characteristic

125

C₂²×C₄₃

C₂×SD₃₂

yes

—

126

C₂²×C₄₃

#509

yes

—

127

C₂×D₄₃

—

128

C₂×D₄₃

—

129

C₂×D₄₃

—

130

C₂×D₄₃

—

131

C₂×D₄₃

—

132

C₄×C₄₃

—

133

C₄×C₄₃

#392

yes

characteristic

134

C₄×C₄₃

#447

yes

characteristic

135

C₄×C₄₃

#459

yes

characteristic

136

C₄×C₄₃

#496

yes

characteristic

137

Dic₄₃

—

138

Dic₄₃

—

139

C₂²×SD₃₂

—

140

C₂×#493

—

141

C₂×#357

—

142

#1969

—

143

#1374

D₄₃

yes

characteristic, complemented

144

C₂×C₄₃

#2011

yes

characteristic

145

C₂×C₄₃

#2187

yes

—

146

C₂×C₄₃

#2207

yes

—

147

C₂×C₄₃

#2248

yes

characteristic

148

C₂×C₄₃

#2250

yes

characteristic

149

D₄₃

—

150

C₂²×Q₁₆

—

151

C₂²×D₈

—

152

C₂²×D₈

—

153

C₂×#127

—

154

C₂×SD₃₂

—

155

C₂×SD₃₂

—

156

C₂×SD₃₂

—

157

C₂²×C₁₆

C₂×D₄₃

yes

—

158

#493

—

159

C₂×#107

—

160

C₂×#103

—

161

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

162

#391

—

163

#357

—

164

C₄₃

#13328

yes

characteristic, complemented, Sylow

165

C₂²×Q₈

—

166

C₂²×D₄

—

167

C₂²×D₄

—

172

—

168

C₂×Q₁₆

—

169

C₂×Q₁₆

—

170

C₂×Q₁₆

—

171

C₂×Q₁₆

—

172

C₂×D₈

—

173

C₂×D₈

—

174

C₂×D₈

—

175

C₂×D₈

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂×D₈

—

179

C₂×D₈

—

172

—

180

C₂×D₈

—

172

—

181

C₂²×C₈

D₁₇₂

yes

characteristic

182

C₂²×C₈

C₂²×D₄₃

yes

characteristic

183

#127

—

184

#127

—

172

—

185

C₂×C₄⋊C₄

—

186

C₂×C₄²

D₁₇₂

yes

characteristic

187

SD₃₂

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

190

C₂×C₁₆

D₁₇₂

yes

complemented

191

#107

—

192

#103

—

172

—

193

C₄×C₈

—

194

#95

—

172

—

195

C₂⁴

—

172

—

196

C₂×Q₈

—

197

C₂×Q₈

—

172

—

198

C₂×Q₈

—

172

—

199

C₂×Q₈

—

172

—

200

C₂×Q₈

—

172

—

201

C₂×Q₈

—

172

—

202

C₂×D₄

—

203

C₂×D₄

—

344

—

204

C₂×D₄

—

344

—

205

C₂×D₄

—

172

—

206

C₂×D₄

—

172

—

207

C₂×D₄

—

172

—

208

C₂×D₄

—

172

—

209

C₂×D₄

—

172

—

210

C₂×D₄

—

172

—

211

C₂²×C₄

—

172

—

212

C₂²×C₄

—

172

—

213

C₂²×C₄

D₃₄₄

yes

—

214

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

215

Q₁₆

—

216

Q₁₆

—

172

—

217

D₈

—

218

D₈

—

219

D₈

—

172

—

220

D₈

—

172

—

221

D₈

—

172

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

D₃₄₄

yes

—

225

C₂×C₈

C₂×D₁₇₂

yes

—

226

C₂×C₈

D₄×D₄₃

yes

characteristic

227

C₂×C₈

D₄×D₄₃

yes

—

228

C₂×C₈

#10621902

yes

characteristic

229

C₄⋊C₄

—

172

—

230

C₄⋊C₄

—

172

—

231

C₄²

—

232

C₄²

—

233

C₁₆

—

234

C₂³

—

344

—

235

C₂³

—

344

—

236

C₂³

—

344

—

237

C₂³

—

344

—

238

C₂³

—

172

—

239

C₂³

C₂×D₃₄₄

yes

characteristic

240

Q₈

—

344

—

241

Q₈

—

344

—

242

Q₈

—

172

—

243

Q₈

—

172

—

244

D₄

—

344

—

245

D₄

—

344

—

246

D₄

—

344

—

247

D₄

—

172

—

248

D₄

—

172

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

344

—

252

C₂×C₄

—

344

—

253

C₂×C₄

—

344

—

254

C₂×C₄

—

344

—

255

C₂×C₄

—

172

—

256

C₂×C₄

#13063270

yes

complemented

257

C₂×C₄

#13063295

yes

characteristic

258

C₂×C₄

#13063300

yes

characteristic

259

C₂×C₄

#13063322

yes

characteristic

260

C₂×C₄

C₂×D₃₄₄

yes

characteristic

261

C₂×C₄

#13063353

yes

characteristic

262

C₂×C₄

#13063353

yes

characteristic

263

C₈

—

264

C₈

#13063295

yes

—

265

C₈

#13063300

yes

—

266

C₂²

—

344

—

267

C₂²

—

344

—

268

C₂²

—

688

—

269

C₂²

—

688

—

270

C₂²

—

688

—

271

C₂²

#14583035

yes

characteristic

272

C₂²

#14583095

yes

characteristic

273

C₂²

#14583276

yes

characteristic

274

C₂²

C₂×#13063270

yes

—

275

C₂²

#14583337

yes

—

276

C₄

—

277

C₄

—

344

—

278

C₄

—

688

—

279

C₄

#14582809

yes

characteristic

280

C₄

#14583035

yes

characteristic

281

C₄

#14583095

yes

characteristic

282

C₄

#14583288

yes

characteristic

283

C₂

—

688

—

284

C₂

#19135668

yes

characteristic

285

C₂

#19136526

yes

—

286

C₂

#19136636

yes

—

287

C₂

#19136851

yes

characteristic

288

C₂

#19136861

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₄₄
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1374	C₂
socle	C₂³×C₄₃	C₂×D₈
prime radical	C₂×#14583276	C₂
hypercenter	#1374	D₄₃
hypocenter	C₄₃	#13328
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₃₄₄

commutator, cosocle

C₂²×C₈×C₄₃

C₂³

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#1374

C₂

socle

C₂³×C₄₃

C₂×D₈

C₂

D₄₃

C₄₃

G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
1. C₂²×#13063270	C₂	semidirect
3. C₂×#14582701	C₂	semidirect
4. #19135456	C₂	semidirect
5. C₄₃×#1374	C₂	semidirect
26. C₂×Dic₁₇₂	D₄	semidirect
48. C₂×C₁₆×C₄₃	D₄	semidirect
97. C₂×C₄×C₄₃	SD₃₂	semidirect
143. #1374	D₄₃	semidirect
164. C₄₃	#13328	semidirect
190. C₂×C₁₆	D₁₇₂	semidirect
256. C₂×C₄	#13063270	semidirect

H ≅ G/N

type

1. C₂²×#13063270

C₂

semidirect

3. C₂×#14582701

C₂

semidirect

4. #19135456

C₂

semidirect

5. C₄₃×#1374

C₂

semidirect

26. C₂×Dic₁₇₂

D₄

semidirect

48. C₂×C₁₆×C₄₃

D₄

semidirect

97. C₂×C₄×C₄₃

SD₃₂

semidirect

143. #1374

D₄₃

semidirect

164. C₄₃

#13328

semidirect

190. C₂×C₁₆

D₁₇₂

semidirect

256. C₂×C₄

#13063270

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13063270	2
C₂×#14583276	2
C₂×#14582701	2
#19135456	2
C₄₃×#1374	2
#13328	43

subgroup

index

C₄₃×#1374

Subgroups — #25015447

Conjugacy classes of subgroups

Complements

Maximal subgroups